7.5 Parts of Similar Triangles

Slides:

Advertisements

Similar presentations

Honors Geometry Section 8. 5

Advertisements

7-5 Parts of Similar Triangles You learned that corresponding sides of similar polygons are proportional. Recognize and use proportional relationships.

Warm Up Find the unknown length for each right triangle with legs a and b and hypotenuse c. NO DECIMALS 5. b = 12, c =13 6. a = 3, b = 3 a = 5.

Tuesday, February 2 Essential Questions

Objectives Justify and apply properties of 45°-45°-90° triangles.

Congruence and Similarity

JRLeon Geometry Chapter 11.3 HGSH Lesson 11.3 (603) Suppose I wanted to determine the height of a flag pole, but I did not have the tools necessary. Even.

7.1 Geometric Mean.  Find the geometric mean between two numbers  Solve problems involving relationships between parts of right triangles and the altitude.

8-1 Geometric Mean p. 537 You used proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles. Find the geometric.

5.1 Bisectors, Medians, and Altitudes. Objectives Identify and use ┴ bisectors and  bisectors in ∆s Identify and use medians and altitudes in ∆s.

6.3 Use Similar Polygons. Objectives IIIIdentify similar polygons SSSSolve problems using proportions with similar polygons.

Indirect Measurement and Additional Similarity Theorems 8.5.

SECTION 8.1 GEOMETRIC MEAN. When the means of a proportion are the same number, that number is called the geometric mean of the extremes. The geometric.

9.1 (old geometry book) Similar Triangles

Geometric and Arithmetic Means

Lesson 7-1 Geometric Means Theorem 7.1 If the altitude is drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two.

7.3 Use Similar Right Triangles

Using Similar Figures 4-5. Vocabulary Indirect measurement- a method of using proportions to find an unknown length or distance in similar figures.

Special Right Triangles

EXAMPLE 1 Finding Area and Perimeter of a Triangle Find the area and perimeter of the triangle. A = bh 1 2 P = a + b + c = (14) (12) 1 2 =

Special Right Triangles 5.1 (M2). What do you know about Similar Triangles?  Corresponding Angles are Congruent  Sides are proportional  Since the.

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

Proportional Parts of a Triangle Proportional Perimeters Theorem If two triangles are similar, then the perimeters are proportional to the measures of.

5-Minute Check on Lesson 6-4 Transparency 6-5 Click the mouse button or press the Space Bar to display the answers. Refer to the figure 1.If QT = 5, TR.

Proportional Parts Advanced Geometry Similarity Lesson 4.

Sec: 6.5 Sol:  If two triangles are similar, then the _____________ are proportional to the measures of corresponding sides. Remember: The perimeter.

6.3 Similar Triangles.

Lesson Menu Main Idea and New Vocabulary NGSSS Key Concept:Similar Polygons Example 1:Identify Similar Polygons Example 2:Find Missing Measures Key Concept:Ratios.

Similar Polygons. A B C D E G H F Example 2-4a Rectangle WXYZ is similar to rectangle PQRS with a scale factor of 1.5. If the length and width of rectangle.

Entry Task  Find the value of x in each figure  x 4 x 6 14.

9.1 Similar Right Triangles Geometry. Objectives  Solve problems involving similar right triangles formed by the altitude drawn to the hypotenuse of.

6.1 Ratios, Proportions and Geometric Mean. Objectives WWWWrite ratios UUUUse properties of proportions FFFFind the geometric mean between.

Warm Up Find the area of each figure. Give exact answers, using  if necessary. 1. a square in which s = 4 m 2. a circle in which r = 2 ft 3. ABC with.

Warm Up For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form Simplify expression. 3.

Area of Triangles Section 8.4. Goal Find the area of triangles.

EXAMPLE 3 Find the area of an isosceles triangle

Corresponding Parts of Similar Triangles

7.5 Parts of Similar Triangles

Warm-up Solve for x x x-3 4 x+6 x+1 x

5-6 to 5-7 Using Similar Figures

Similarity Postulates

1. Are these triangles similar? If so, give the reason.

Similar Triangles.

7.3 Similar Triangles.

7-5: Parts of Similar Triangles

7-5 Parts of Similar Triangles

6.5 Parts of Similar Triangles

Use the Triangle Bisector Theorem.

If QT = 5, TR = 4, and US = 6, find QU.

Class Greeting.

Main Idea and New Vocabulary Key Concept: Similar Polygons

Chapter 7 Lesson 5: Parts of Similar Triangles

Parts of Similar Triangles

Starter(s): Solve the proportion A. 15 B C. D. 18

LESSON 8–1 Geometric Mean.

6.5 Parts of Similar Triangles

8-1: Similarity in Right Triangles

7.5 : Parts of Similar Triangles

7.3 Use Similar Right Triangles

Corresponding Parts of Similar Triangles

LESSON 8–1 Geometric Mean.

Parts of Similar Triangles

Parts of Similar Triangles

7.3 Special Right Triangles

2.5 Similar Figures Essential Question: How can you determine if two figures are similar or not? Trapezoids ABCD and EFGH are congruent. Congruent: (same.

Five-Minute Check (over Chapter 7) Mathematical Practices Then/Now

Using Similar Figures ABC is similar to DEF. Find the value of c. =

Presentation transcript:

7.5 Parts of Similar Triangles

Objectives Recognize and use proportional relationships of corresponding perimeters of similar triangles Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles

Proportional Perimeters Theorem If two Δs are similar, then the perimeters are proportional to the measures of the corresponding sides.

Example 1: C If and find the perimeter of Let x represent the perimeter of The perimeter of

Example 1: Proportional Perimeter Theorem Substitution Cross products Multiply. Divide each side by 16. Answer: The perimeter of

Your Turn: If and RX = 20, find the perimeter of R Answer:

Special Segments of ~ Δs Theorem 6.8 In ~ Δs, corresponding altitudes are proportional to the measures of the corresponding sides Theorem 6.9 In ~ Δs, corresponding angle bisectors are proportional to the measures of the corresponding sides Theorem 6.10 In~ Δs, corresponding medians are proportional to the measures of the corresponding sides

Example 2: In the figure, is an altitude of and is an altitude of Find x if and K

Example 2: Write a proportion. Cross products Divide each side by 36. Answer: Thus, JI = 28.

Your Turn: In the figure, is an angle bisector of and is an angle bisector of Find x if N Answer: 17.5

Example 3: The drawing below illustrates two poles supported by wires. , , and Find the height of the pole .

Example 3: are medians of since and If two triangles are similar, then the measures of the corresponding medians are proportional to the measures of the corresponding sides. This leads to the proportion measures 40 ft. Also, since both measure 20 ft. Therefore,

Example 3: Write a proportion. Cross products Simplify. Divide each side by 80. Answer: The height of the pole is 15 feet.

Your Turn: The drawing below illustrates the legs, of a table. The top of the legs are fastened so that AC measures 12 inches while the bottom of the legs open such that GE measures 36 inches. If BD measures 7 inches, what is the height h of the table? Answer: 28 in.

Assignment Geometry Pg. 320 #10 – 24 Pre-AP Geometry Pg. 320 #10 – 28